Problem: Simplify the following expression: $r = \dfrac{1}{7a} - \dfrac{5}{9a}$
Explanation: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $7a$ and $9a$ $\lcm(7a, 9a) = 63a$ $ r = \dfrac{9}{9} \cdot \dfrac{1}{7a} - \dfrac{7}{7} \cdot \dfrac{5}{9a} $ $r = \dfrac{9}{63a} - \dfrac{35}{63a}$ $r = \dfrac{9 -35}{63a}$ $r = \dfrac{-26}{63a}$